(source: https://www.cambridgeassociates.com/wp-content/uploads/2015/05/Public-USVC-Benchmark-2014-Q4.pdf …)
In the linked article, the optimal amount to invest in an asset is (mu-r)/sigma^2. If mu = r (if the asset has no higher an average rate of return than cash), this implies the optimal amount to invest is zero. What am I missing?
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The math there is wrong: 1. log((1-f)r)!= (1-f)r. 2. E(log(a)+lob(b))!=E(log(a))+E(log(b)) 3. They seem to be computing based on arithmetic growth i.e. a 5% increase is .05 instead of 1.05 and 5% drop is -.05 instead of .95. This is wrong and log will blow up on neg numbers.
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So what is the optimal amount to invest in a stock with positive variance but zero (risk-adjusted) drift?
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